1. Field of the Invention
The present invention relates to an optical method for imaging through a scattering medium in which a fit is made to an inhomogeneous diffusion model. The method provides a simple means to separate the absorption and scattering contributions of inhomogeneities.
2. Background of the Invention
The ability to optically imaging through a scattering medium is of great interest. Potential applications are the non-destructive localization of inclusions or defects in scattering materials such as composites or polymers and the detection of parasites in fish or meat produce. A main target application is breast cancer detection, which is currently carried out mostly with X-rays. X-rays provide good resolution images but with poor contrast between healthy and cancerous tissues. They are also considered as potentially hazardous to humans. This explains that optical imaging through scattering media is an area of research that has created enormous interest.
Obtaining optical images of the interior of a scattering medium such as a breast is complicated by the extensive scattering of light in such a medium, which results in blurring of the image. As a result of such scattering, the trajectory of a photon (i.e. a light particle) can be predicted only on a statistical basis, each photon propagating along a random-like path as shown in FIG. 1. In addition to being randomly redirected by scattering events, each photon also has a probability of being absorbed by the medium.
In a slab of material that is highly scattering and weakly absorbing, such as the human breast, most photons are reflected towards the entrance surface after traveling only a few millimeters into the medium. Other photons are absorbed by the medium or are transmitted to the output surface where they can be detected. For a breast of typical thickness and optical parameters, 0.01 to 1% of the injected photons at a wavelength around 800 nm are transmitted to the output surface.
The transmitted photons can be separated into three categories: ballistic photons that reach the output surface without be scattered, snake photons that are scattered slightly and maintain a fairly rectilinear trajectory, and diffuse photons that are widely scattered and cover a considerable volume element before emerging. FIG. 1 illustrates each of these categories. Ballistic photons do not experience any scattering event and therefore have the potential to produce a very clear image of the breast interior. Unfortunately, for typical breast thickness and optical parameters, no ballistic photons are transmitted. Snake photons have a nearly rectilinear trajectory, and are sufficient in number to produce a relatively clear image. Diffuse photons provide image information of poor quality due to their degree of scattering. Therefore, researchers have focused their efforts on detecting the snake photons and excluding the diffuse photons. Typically this has been done by utilizing time gating techniques.
Time gating is implemented by sending ultra-short laser pulses inside of a scattering medium. When an ultra-short laser pulse is injected at the surface of a scattering medium its component photons propagate along different trajectories. The different times of propagation lead to the emergence from the scattering medium of a temporally broadened pulse which is called the diffusion pulse or the diffusion curve as illustrated in FIG. 1. For a breast of typical thickness and optical parameters, the duration of the diffusion pulse can be as large as several nanoseconds, which is more than 1000 times the width of the entrance pulse, typically less than 1 picosecond. The initial portion of the diffusion curve corresponds to the snake photons with a shorter path, whereas the remainder corresponds to the diffuse photons. By their shorter arrival time at the detector, the snake photons can be isolated and used to construct the image. This technique, known as time gating, created a resurgence of interest in optical mammography in the early 1990s.
Using only snake photons allows the user to generate images with better spatial resolution. However, the relative noise level increases significantly because much fewer photons are detected in this way. This method also does not allow for the determination of the scattering and absorption properties of an inclusion detected within a scattering medium. In order to overcome these limitations, researchers have looked for ways to use the information carried by all photons, i.e., by the whole of the diffusion curve, to obtain images through scattering media, as follows.
The shape and amplitude of the diffusion curve depend on the scattering and absorption properties of the scattering medium. A theoretical model, the diffusion model, can be used to describe the diffusion curve for homogeneous and optically thick slabs having uniform structure throughout. This model is appropriate in the specific case of light transmitted through a human breast. It involves a limited number of parameters that characterize the scattering and absorption properties of the scattering medium. The optical properties of scattering media such as human tissues are usually characterized by three parameters. The absorption coefficient .mu..sub.a is the probability of a photon being absorbed per infinitesimal pathlength. The scattering coefficient .mu..sub.s is the probability of the photon being scattered per infinitesimal pathlength. Finally, the third parameter is the anisotropy factor g which describes the average change in propagation direction associated with the scattering process. In addition to these three parameters, it is useful to define the reduced scattering coefficient as EQU .mu..sub.s '.ident..mu..sub.s (1-g)
representing the average distance over which a photon sustains a sufficient number of scattering events to randomize its direction of propagation. The reduced scattering coefficient is the isotropic equivalent of the scattering coefficient and is applicable to the case of thick scattering media. The quantities .mu..sub.a and .mu..sub.s ' are the two main optical parameters that describe the light propagation in thick scattering media. Those two parameters appear in the diffusion model suitable for a homogeneous scattering slab.
Researchers have tried to extract imaging information from the whole of the diffusion curve through curve fitting. Curve fitting is a general numerical technique which includes adjusting a mathematical expression on experimental data. The idea of using curve fitting in optical mammography is not new. The diffusion model has been used as the analytical expression (valid only in homogeneous cases), and curve fitting was employed to smooth the experimental data to reduce the level of noise in the time gating approach.
Since the output of the curve fitting is the parameters of the analytical model, and since some of the parameters are the two optical coefficients .mu..sub.a and .mu..sub.s ', the process allows for the separation of information about the scattering and absorption in the probed region. Curve fitting can therefore be performed to obtain those optical parameters and to plot their spatial distributions. As a result, more information is obtained since two output images are created instead of only one. Because the analytical expression used in the curve fitting process is the diffusion model, which is valid only in the homogeneous case, problems develop. In particular, non-uniformity in an inhomogeneous medium results in non-uniformity in the spatial distribution of the optical parameters .mu..sub.a and .mu..sub.s '. Since non-uniformity is incorrectly described by the model, incorrect .mu..sub.a and .mu..sub.s ' distribution are obtained. As a result, an actual spatial variation of the scattering coefficient may result in a variation of .mu..sub.a as outputted by data processing and vice-versa. The foregoing method does not discriminate correctly between scattering and absorbing effects.
There is a need for a method which provides a simple mathematical expression which describes the effect of inclusions on the diffusion curves which will be applicable to generate images of thick inhomogeneous scattering media.